Simulation of potential evapotranspiration values based on vine copula

Abstract

Vine copula had a great impact on the study and analysis of dependence structures in various sciences. In multivariate analyses with dimensions of more than two variables, it is associated with computational complexities that solve vine copulas and these problems. In this study, in order to provide an approach to simulate potential evapotranspiration based on meteorological parameters in Birjand meteorological station from different family copulas including Rvine, independent R-vine, Gaussian, independent Gaussian, C-vine, C-vine independent, D-vine and D-vine independent were used. In this regard, vine copula simulation and conditional density were used. In pair correlation analysis of the studied variables using Kendall's tau statistic, dependence structure confirmed the studied parameters. The results showed a minimum correlation of À0.32 and a maximum of 0.77. The results of Akaike's information criteria (AIC), Bayesian information criteria (BIC) and LogLike statistics in evaluating the performance of vine copula dependency structure introduced the C-vine copula as the superior copula for analysing the pair dependence of the studied variables. By introducing the superior dependency structure and internal copulas, the tree sequence of the pair of values under study was obtained. Pair of simulated values was performed using vine copula. Comparison of Kendall's tau values in both simulation and observation modes showed that Kendall's tau values were close to each other in both modes and were approximately similar. The simulation results of vine copula potential evapotranspiration values and precipitation, temperature and relative humidity values showed 92% efficiency. The efficiency of C-vine copula in dependence analysis and simulation of potential evapotranspiration (PET) values is very high, which shows the ability of vine family copulas in multivariate analysis.

Application of vine copulas to estimate dew point temperature

“…Various studies in the field of simulation and modeling of different meteorological and hydrological parameters show that the copula function has recently been considered by various researchers. Copula-based simulation has best acceptable certainty due to the involvement of proportional data distribution in modeling and simulation as well as the use of conditional density of copula functions (De Michele and Salvadori, 2003;De Michele et al 2005;Salvadori and De Michele, 2004, 2007, and 2010Salvadori et al, 2007 andTahroudi et al, 2020a&b;Khashei-Siuki et al 2021). Copula functions increase the accuracy of simulations and improve their certainly by considering the marginal distribution of data in simulations.…”

“…Vine copulas with a wide variety of tree sequences allow the selection of different structures that improve the results. Khashei-Siuki et al (2021) to simulation of potential evapotranspiration at Birjand meteorological station, Iran used vine copulas. The results of the simulation of the potential evapotranspiration given by precipitation, air temperature and relative humidity using vine copulas showed a NSE= 92%.…”

Integrated Drought Index based on Vine Copula Modelling

“…(2021) and Khashei‐Siuki et al . (2021) used vine copula to simulate flood hydrograph and potential evapotranspiration model, respectively, in their studies. They found that the efficiency of vine copula in dependence analysis was good and accurate.…”

“…The complete freedom to select bivariate copula in each step of hierarchical structure provides elevated flexibility in vine copula based multivariate dependence modelling than traditional copulas (Ni et al, 2020). Based on this aspect, Tahroudi et al (2021) and Khashei-Siuki et al (2021) used vine copula to simulate flood hydrograph and potential evapotranspiration model, respectively, in their studies. They found that the efficiency of vine copula in dependence analysis was good and accurate.…”